How to use this calculator
- Enter the deviations. Enter the measured ΔX and ΔY of the feature axis from its true (basic) location.
- Enter the position tolerance. Enter the position tolerance from the feature control frame (a diameter).
- Apply MMC if specified. If the callout has an MMC modifier, choose hole or pin and enter the MMC size and the actual measured size for the bonus tolerance.
- Read pass/fail. Read the true position diameter, the bonus, the allowed total, and whether the feature is in tolerance.
How it works
True position reports how far a feature's axis is from where the
drawing says it should be, as the diameter of the tolerance zone it actually needs:
TP = 2 · √(ΔX² + ΔY²)
where ΔX and ΔY are the deviations of the measured axis
from its basic (true) location. Because position tolerance is a cylindrical
(diametral) zone, the radial deviation is doubled. For callout interpretation,
see the true position guide and the
GD&T symbols chart.
When the callout carries a maximum material condition (M)
modifier, the feature earns bonus tolerance as it departs from MMC.
For a hole the bonus is actual − MMC; for a pin it is
MMC − actual. The feature is acceptable when the true position diameter
is within the position tolerance plus that bonus. If you only need the material-condition
allowance, use the MMC bonus
tolerance calculator.
Worked example
Verified against the live calculator
A hole's axis is measured 0.1 mm off in X and 0.1 mm off in Y. The true position is
2 × √(0.1² + 0.1²) ≈ 0.283 mm — within a 0.3 mm position tolerance, so
it passes at RFS. If the callout is at MMC with a 10.0 mm minimum hole that actually
measures 10.2 mm, the bonus is 0.2 mm, so the allowed tolerance becomes 0.5 mm — a
comfortable margin. The calculator shows exactly this.
Frequently asked questions
How do you calculate true position?
True position is the diameter of the smallest tolerance zone that contains the feature axis: Ø = 2 × √(ΔX² + ΔY²), where ΔX and ΔY are the measured deviations of the axis from its true (basic) location.
Why multiply by 2?
ΔX and ΔY give the radial distance of the axis from true position. The GD&T position tolerance is a diameter (a cylindrical zone), so the radius is doubled.
What is MMC bonus tolerance?
When the feature control frame carries a maximum-material-condition (MMC) modifier, the position tolerance grows as the feature departs from MMC. The bonus equals that departure and is added to the stated position tolerance.
How is the bonus different for a hole versus a pin?
For a hole (internal feature) MMC is the smallest size, so bonus = actual − MMC (a bigger hole earns more). For a pin (external feature) MMC is the largest size, so bonus = MMC − actual (a smaller pin earns more).
How do I check pass or fail?
The feature passes when the true position diameter is less than or equal to the allowed tolerance — the stated position tolerance plus any MMC bonus.
What about three datums?
ΔX and ΔY are the in-plane deviations from the basic location, measured in the datum reference frame. Establish the part on its datums first; the deviations you enter are relative to the true position in that frame.
Method & assumptions
- Two-dimensional (X-Y) position in a single datum reference frame; establish the part on its datums before measuring.
- MMC bonus is the linear departure from the maximum-material size; LMC works the same way with the limits reversed.
- For composite tolerances (PLTZF/FRTZF) the two tiers are checked separately — that's a dedicated calculation.